Exact Self-dual Soliton Solutions in a Gauged O(3) Sigma Model with Anomalous Magnetic Moment Interaction

Abstract

It is shown that a gauged nonlinear $O(3)$ sigma model with anomalous magnetic moment interaction in $2+1$ dimensions is exactly integrable for static, self-dual field configurations. The matter fields are exactly equivalent to those of the usual ungauged nonlinear $O(3)$ sigma model. These static soliton solutions can be mapped into an Abelian purely magnetic vortex solutions through a suitable reduction of the non-Abelian gauge group. A relativistic Abelian model in $2+1$ dimensions is also presented where these purely magnetic vortices can be realized.